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We propose a formal approach for relating abstract separation logic library specifications with the trace properties they enforce on interactions between a client and a library. Separation logic with abstract predicates enforces a resource discipline that constrains when and how calls may be made between a client and a library. Intuitively, this can enforce a protocol on the interaction trace. This intuition is broadly used in the separation logic community but has not previously been formalised. We provide just such a formalisation. Our approach is based on using wrappers which instrument library code to induce execution traces for the properties under examination. By considering a separation logic extended with trace resources, we prove that when a library satisfies its separation logic specification then its wrapped version satisfies the same specification and, moreover, maintains the trace properties as an invariant. Consequently, any client and library implementation that are correct with respect to the separation logic specification will satisfy the trace properties.
Ultrafinitism postulates that we can only compute on relatively short objects, and numbers beyond certain value are not available. This approach would also forbid many forms of infinitary reasoning and allow to remove certain paradoxes stemming from
Recursive definitions of predicates are usually interpreted either inductively or coinductively. Recently, a more powerful approach has been proposed, called flexible coinduction, to express a variety of intermediate interpretations, necessary in som
Abstract interpretation is a well-established technique for performing static analyses of logic programs. However, choosing the abstract domain, widening, fixpoint, etc. that provides the best precision-cost trade-off remains an open problem. This is
In program synthesis there is a well-known trade-off between concise and strong specifications: if a specification is too verbose, it might be harder to write than the program; if it is too weak, the synthesised program might not match the users inte
We study the synthesis of policies for multi-agent systems to implement spatial-temporal tasks. We formalize the problem as a factored Markov decision process subject to so-called graph temporal logic specifications. The transition function and the s